Data carriers, preferably magnetic tapes, diskettes, CD ROM, DVD, etc., are used for automatic storage of large amounts of data. The data carriers are then accommodated in cassettes, in which a number of such cassettes are accommodated in a magazine. A robot unit serves to remove a selected cassette from the receptacle of the magazine or insert it into this receptacle. The magazine with receptacles for cassettes and the robot unit are controlled to move, relative to each other, for this purpose, in order to position the robot unit and the selected receptacle of the magazine in aligned fashion for replacement. Such devices are on the market, for example, under the names Autoloader and Tape-Library. An example of such an autoloader is shown in DE 100 55 624 C2. In order to change the cassettes in the change position from the corresponding receptacle or to the corresponding receptacle, an exact alignment of the selected receptacle in the robot unit is required. This exact alignment requires high mechanical precision in the drive and in the guide of the magazine and the robot unit, which results in significant technical expense, especially with a large storage capacity, i.e., with a large number of cassettes.